Scalars
Non-directional quantities are called scalar.
Or
Quantities having only are scalars.
Examples;
Mass, length, work, speed, power, distance, etc.
Vectors
Directional quantities are called vectors.
Or
Quantities having magnitudes as well as direction and obey laws of vector algebra.
Examples;
Displacement, velocity, acceleration, force, electric field, momentum, torque, etc.
Scalars are added, subtracted, multiplied and divided by simple arithmetic rules.
Vectors are added, subtracted and multiplied by special rules.
Representation of vectors
Vectors can be represented in two ways;
Analytical or symbolic representation
Graphical representation
1. Analytical or symbolic representation
Symbolically a vector is represented by a letter with an arrow on the top or bold letters such
as;
A B OR A B.
Magnitude of a vector is represented by light face letter like A, B, F etc. or by modulus like |
A| |B| |F| etc.
2. Graphical representation
Graphically a vector is represented by a straight a line with an arrow head.
The point of a line is called tail.
The ending point of a line having arrow is called head.
Length of a line represents the magnitude and arrow shows the direction.
Vector changes when;
i. Its magnitude changes only.
ii. Its direction changes only.
, A vector does not change when;
i. It is displaced parallel to itself.
ii. It is rotated at an angle such that;
Angle= n × 2π
Angle between two vectors;
Angle between two vectors is only measured when their heads or their tail are at the same point.
Types of vectors
i. Equal vectors
Same magnitude
Same direction
ii. Negative vector
Same magnitude
Opposite direction
iii. Free vector
Vector which can be displaced parallel to itself.
It is not fixed to the origin.
Non-directional quantities are called scalar.
Or
Quantities having only are scalars.
Examples;
Mass, length, work, speed, power, distance, etc.
Vectors
Directional quantities are called vectors.
Or
Quantities having magnitudes as well as direction and obey laws of vector algebra.
Examples;
Displacement, velocity, acceleration, force, electric field, momentum, torque, etc.
Scalars are added, subtracted, multiplied and divided by simple arithmetic rules.
Vectors are added, subtracted and multiplied by special rules.
Representation of vectors
Vectors can be represented in two ways;
Analytical or symbolic representation
Graphical representation
1. Analytical or symbolic representation
Symbolically a vector is represented by a letter with an arrow on the top or bold letters such
as;
A B OR A B.
Magnitude of a vector is represented by light face letter like A, B, F etc. or by modulus like |
A| |B| |F| etc.
2. Graphical representation
Graphically a vector is represented by a straight a line with an arrow head.
The point of a line is called tail.
The ending point of a line having arrow is called head.
Length of a line represents the magnitude and arrow shows the direction.
Vector changes when;
i. Its magnitude changes only.
ii. Its direction changes only.
, A vector does not change when;
i. It is displaced parallel to itself.
ii. It is rotated at an angle such that;
Angle= n × 2π
Angle between two vectors;
Angle between two vectors is only measured when their heads or their tail are at the same point.
Types of vectors
i. Equal vectors
Same magnitude
Same direction
ii. Negative vector
Same magnitude
Opposite direction
iii. Free vector
Vector which can be displaced parallel to itself.
It is not fixed to the origin.
